Current Transform and Mesh Analysis

[naosyth]

1 Problem Statement:

2 Relevant Equations

KVL
KCL
Ohm's Law

3 Attempt at Solution

I solved Problem 4.2, which was just mesh analysis on the original problem. I got the correct answers, indicated by F.A. The problem I am having with 4.3 is how to redraw the circuit with the indicated changes. When I redraw it, I am left with only two meshes, but I need to find three mesh currents. All I really need is to be pointed in the right direction on how to redraw the circuit, and where the three mesh currents would be. I have been working on this for hours and have tried too many things to list it all here...

Edit: This is where I am at so far:

Ignore the equations under the circuit, that was just me trying random ideas...

 

[Simon Bridge]

I don't see why you need three mesh currents.

 

[naosyth]

I don't either, that's the problem. The question says the find the mesh currents, and lists three answers. Without the current transform, then it is an easy problem. With the transform though, I am quite confused...

 

[naosyth]

Aha! I got it! When you do the transformation, you get two meshes, but then you apply KCL with one of the meshes and the 13A current supply from the original circuit to get the third mesh current. My professor replied to my email shortly after I did this, and confirmed that this is the correct solution! It feels good finally solving this, after 4 hours!

 

[Simon Bridge]

Yeah - you only needed to find three currents.
In the first version of the problem, they corresponded to the meshes.